Sen. Susan Collins of Maine said Friday she will support Senate Republicans’ $1.4 trillion-plus tax-cut bill, all but ensuring that GOP leaders do indeed have enough support to pass the legislation as they indicated earlier in the day.

“As revised, this bill will provide much-needed tax relief and simplification for lower- and middle-income families, while spurring the creation of good jobs and greater economic growth,” Ms. Collins said.

Republican leaders had been dealing with about a half-dozen holdouts, but those senators have been steadily coming off the fence to announce their support Friday, and Majority Leader Mitch McConnell says the GOP has enough votes to pass the bill.

Ms. Collins said she was able to secure several key agreements ahead of the announcement on her vote.

She said leaders agreed to restore a property tax deduction of up to $10,000 that had been on the chopping block, which mirrors compromise language GOP leaders also struck in the House with some blue-state Republicans.

Ms. Collins also said she secured language to lower an income threshold for two years for people claiming a deduction on unreimbursed medical expenses, and that she was able to ax language forbidding “catch-up” retirement account contributions for certain public employees and nonprofit workers.

She also said Mr. McConnell has committed to support the passage of health care legislation to fund Obamacare cost-sharing subsidies and deal with high-risk pools for people with pre-existing conditions in separate legislation by the end of the year.

Ms. Collins said those health care measures would help offset any associated premium spikes resulting from the Senate bill’s inclusion of a repeal of Obamacare’s individual mandate.

Shortly before Ms. Collins announced her support, Mr. McConnell and Speaker Paul D. Ryan also issued a joint statement that allayed other concerns she had that pay-as-you-go rules could trigger cuts to programs like Medicare if the tax bill as outlined becomes law.

Mr. McConnell and Mr. Ryan said Congress would find a way to waive the law if it came to that, and said it’s never been enforced since its enactment in 2010.

“There is no reason to believe that Congress would not act again to prevent a sequester, and we will work to ensure these spending cuts are prevented,” the leaders said.